Smoothed particle magnetohydrodynamics - III. Multidimensional tests and the B = 0 constraint
Smoothed particle magnetohydrodynamics - III. Multidimensional tests and the B = 0 constraint
复制标题
平滑粒子磁流体动力学 - III。
DOI：
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发表时间：
2005
期刊：
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通讯作者：
J. Monaghan
中科院分区：
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作者：
Daniel J. Price;J. Monaghan
在之前的两篇论文(Price&Monaghan 2004a，b)(论文I，II)中，我们描述了一种使用光滑粒子流体动力学(SPH)方法求解磁流体动力学(MHD)方程的算法。该算法使用耗散项来捕捉激波，并在绝热和等温MHD中的一维问题上进行了广泛的测试。在这篇文章中，我们研究了算法的多维方面，提炼了文献I和II中考虑的许多方面，并特别注意了代码保持与磁场相关的r·B=0约束的能力。特别地，我们实现了Dedner等人最近提出的一种双曲线散度清理方法。(2002)，结合文献I和II中推导出的存在非零磁散度时MHD方程的一致表述，还研究了保持无散度条件的各种投影方法。最后，针对用于测试最近基于网格的MHD代码的广泛的多维问题，对该算法进行了测试。这些测试的一个特殊发现是，在SPMHD中，发散误差的大小取决于用于计算粒子性质的相邻粒子的数量，并且仅弱地依赖于粒子总数。虽然算法仍有许多改进之处，但我们的结果表明，该方法已经成熟，可以应用于当前理论上感兴趣的问题，如恒星形成问题。
In two previous papers (Price & Monaghan 2004a,b) (papers I,II) we have described an algorithm for solving the equations of Magnetohydrodynamics (MHD) using the Smoothed Particle Hydrodynamics (SPH) method. The algorithm uses dissipative terms in order to capture shocks and has been tested on a wide range of one dimensional problems in both adiabatic and isothermal MHD. In this paper we investigate multidimensional aspects of the algorithm, refining many of the aspects considered in papers I and II and paying particular attention to the code’s ability to maintain the r·B = 0 constraint associated with the magnetic field. In particular we implement a hyperbolic divergence cleaning method recently proposed by Dedner et al. (2002) in combination with the consistent formulation of the MHD equations in the presence of non-zero magnetic divergence derived in papers I and II. Various projection methods for maintaining the divergence-free condition are also examined. Finally the algorithm is tested against a wide range of multidimensional problems used to test recent gridbased MHD codes. A particular finding of these tests is that in SPMHD the magnitude of the divergence error is dependent on the number of neighbours used to calculate a particle’s properties and only weakly dependent on the total number of particles. Whilst many improvements could still be made to the algorithm, our results suggest that the method is ripe for application to problems of current theoretical interest, such as that of star formation.